Wolfram Demonstrations Project

The American Mathematical Monthly problem 10578 considers a sequence defined by recurrence equation

with initial conditions

and asks to show that

is only an integer for prime

This Demonstration uses Mathematica's built-in function RecurrenceTable to generate the sequence and finds

for which

is an integer.

It is easy to find a symbolic solution of the above recurrence equation:

The above fraction is an integer only for prime

by virtue of Wilson's theorem.

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Wilson's Theorem in Disguise